Questions on the mathematical aspects of signal processing. Please consider first if your question might be more suitable for http://dsp.stackexchange.com/

# Questions tagged [signal-processing]

1906 questions

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### FFT bins from exact frequencies

I'm trying to understand a few concepts about Fourier Transforms (mainly in the context of signal processing).
Let's suppose a signal is sampled at 10kHz and that the FFT size is 1000.
If 1000 samples are processed through this FFT (real only,…

Bruno

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### Mathematically inclined books on Signal Processing Theory

First off, i know this may seem off topic but i could not find help in signal processing communities so i was hoping there would be people here who both love mathematics and have interest in signal processing.
I'm an electronics engineering…

nerdy

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### Under what conditions does the "third-order version of Plancherel's theorem" hold?

I have read in a few places that the formula
$$ \int_\mathbb{R} x(t)^3 \, dt \ = \ \int_{\mathbb{R}^2} \hat{x}(f_1)\hat{x}(f_2)\hat{x}(-f_1-f_2) \, d(f_1,f_2) $$
holds (where $\hat{x}$ denotes the Fourier transform of $x$), but without any…

Julian Newman

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### How can I describe the vertical component of a juggling ball's path with a sine wave?

I juggle, and then track the juggling balls.
I want to describe this juggling trick using sine waves. A metronome was used to keep the throws periodic. The video is 120fps, so there are 120 observations per second. The Y-values correspond to the…

Stephen Meschke

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### What does upside down "v" ($\wedge$) mean in this equation?

I have a simple question, but it is hard to google it. I have this equation here:
$$y(t, x) = \sum_{i=1}^{d}(|x_i| \wedge t)^{2}
$$
Here $x$ is a size $d$ signal and $t$ is just a scalar. I am not sure how to read that equation in english... I…

Spacey

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### Potential uses for viewing discrete wavelets constructed by filter banks as hierarchical random walks.

I have some weak memory that some sources I have encountered a long time ago make some connection between random walks and wavelets, but I am quite sure it is not in the same sense.
What I was thinking is to in the matrices representing filtering…

mathreadler

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### Physical interpretation of $L_1$ and $L_2$ norms

In signal analysis, students have no qualms about associating the $L_2$ norm of a square integrable function $f(t)$ as the energy associated with that signal.
A good understanding of whether a function $f(t)$ is a square integrable function is to…

Fraïssé

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### Finding the period of the solution to $y'(x) = y(x) \cdot \cos(x + y(x))$ with Fourier transform; how to interpret complex result?

A question elsewhere on this site asks about detecting the frequency of oscillations in a system defined by differential equations.
The equation is $y'(x) = y(x) \cdot \cos(x + y(x))$. The solution can be found numerically (plot of $y(x)$ over…

Superbest

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### What is a cardinal basis spline?

Wikipedia says:
the normalized cardinal B-splines tend to the Gaussian function
and writes them as "Bk". Meanwhile, cnx.org Signal Reconstruction says:
The basis splines Bn are shown ... as the order increases, the functions approach the…

endolith

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### Describing a Wave

I have this wave in front of me, and I am to describe this into a math description such as its function that is equivalent to representing this wave. I have no idea how to start and could use some detailed guidance if possible, or just how to go…

night owl

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### Is impulse response always differentiation of unit step response of a system?

I was trying to solve a question in which the transfer function of a system was asked, its unit step response was given as:
$$c(t) = 1-10e^{-t}$$
The method that the book followed was to first find out $C(s)$ i.e.
$$\mathcal{L}(c(t)) =…

HIMANK

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### Regarding $x^2-a^2$ inside the argument of dirac delta

My undergraduate system textbook has this property in the appendix
$$\delta(x^2-a^2)=\frac{1}{2|a|}[\delta(x-a)+\delta(x+a)]$$
and I can't seem to derive the result
I tried the following:
$\int_{-\infty}^{\infty}f(x)\delta(x^2-a^2)\, dx$
let…

xbd

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### Wavelets: Cone Of Influence

While reading this paper I came across the term Cone of Influence which is described as
COI is the region of the wavelet spectrum in which edge effects become important
and is defined here as the e-folding time for the autocorrelation of wavelet…

Sektor

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### Karhunen-Loeve expansion of non-centered processes

The typical form of Karhunen-Loeve expansion is on a detrended stochastic process. E.g., let $Y(t)$ be a stochastic process on $[0,T]$, and let $X(t) = Y(t)-\mathbb{E}Y(t)$ with a continuous covariance function $R_X(s,t)$, then there exists a series…

yixianshuiesuan

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### How to fit a curve to a sinusoidal wave

I am wondering how to fit a sinusoidal wave (approximation). I would like to fit it in the form: $y = A\sin(Bx + C) + D$ where $A,\,B,\,C$ and $D$ are constants. The only constants I really care about is A and B so that I can get the amplitude and…

rick

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